Given trinagle ABC whose sides are AB=15 in., AC=25 in., and BC=30 in. Form a point D on the side AB, a line DE i drawn to a pointE on side AC such that angle ADE is equal to angle ABC. If the perimeter of triangle ADE is 28 in., find …

In a diagram of an 2 isosceles triangles, where ABC is a big triangle and a ADE, is just inside the top portion of ABC. Isosceles triangle ABC is similar to a isosceles triangle ADE what is the length of DE, which is the base part …

Let the incircle of triangle $ABC$ be tangent to sides $\overline{BC}$, $\overline{AC}$, and $\overline{AB}$ at $D$, $E$, and $F$, respectively. Prove that triangle $DEF$ is acute. I have tried proving that triangle DEF's angles were …